O'Driscoll suffered concussion in the match and began the 'return to play' medical protocol on Monday.
However, it soon became clear at the start of the process that he was not going to be ready for a return to action for Saturday's third Test in Johannesburg.
O'Driscoll said: "Being a part of the 2009 British & Irish Lions squad has been one of the highlights of my career.
"We were unbeaten leading into the Test matches and it is a shame that the results in the Tests did not go our way but sport comes down to fine margins at times.
"We could easily have won the first two Tests but it wasn't to be," added Ireland's Grand Slam-winning captain.
"I have decided to return home to my family this week after a very long season and to ensure I give myself every opportunity to recouperate."
Jones said: "It is always disappointing to be ruled out of a Test through injury but I am proud of what the squad and I have achieved on the tour.
"Personally, I will always remember playing in the two first Tests and especially running on for my starting debut at Loftus Versfeld. My heart will be with the boys on Saturday."
Gethin Jenkins, who suffered a broken cheekbone in the second Test, was also ruled out of the rest of the tour but he will stay with the tour party.
The Cardiff Blues and Wales prop has a review appointment with the surgeon on Friday. With just one match remaining on the tour, the Lions management will not call for replacement players.
Providing a further medical update, Lions doctor James Robson said: "The two other players who suffered injury in the second Test, Tommy Bowe and Jamie Roberts, continue to be assessed on a daily basis but at this point they are making encouraging progress."